Fast admittance measurement method for piezoelectric leaf cell sensor array in multiphase gas-oil-water flow metering
An apparatus for fluid measurement is disclosed. The apparatus includes a leaf cell sensor having one or more piezoelectric radial components connected to a circumferential component, a first electrode positioned on a distal face of at least one radial component, a second electrode positioned on a proximal face of the at least one radial component, a voltage source having a negative terminal and a positive terminal, the negative terminal being connected to the first electrode and the positive terminal being connected to the second electrode, an electric current measurement device connected to the first and second electrode to measure current flowing between the first and second electrode, and a processor of a computing device that determines, from the measured current, one or more properties of the fluid, where the voltage source couples electrical energy into the one or more piezoelectric radial components at multiple frequencies concurrently.
1. An apparatus for fluid measurement, the apparatus comprising:
a leaf cell sensor having one or more piezoelectric radial components connected to a circumferential component, the one or more radial components and the circumferential component having a distal face and a proximal face;
a first electrode positioned on the distal face of at least one radial component;
a second electrode positioned on the proximal face of the at least one radial component;
a voltage source having a negative terminal and a positive terminal, the negative terminal being connected to the first electrode and the positive terminal being connected to the second electrode;
an electric current measurement device connected to the first and second electrode to measure current flowing between the first and second electrode; and
a processor of a computing device and a non-transitory computer readable medium storing instructions thereon, wherein the instructions, when executed, cause the processor to determine, from the measured current, one or more properties of the fluid,
wherein the voltage source couples electrical energy into the one or more piezoelectric radial components at multiple frequencies concurrently, and
wherein the voltage source comprises a white noise generator having a spectral power density of white gaussian noise with energy content according to a gaussian distribution.
2. The apparatus of claim 1 , wherein the white noise generator has a band-limited spectral power density with energy content concentrated at a particular range of frequencies.
3. The apparatus of claim 1 , where the circumferential component has a shape based on contour segments of the canonical Rhodonea conformal mapping geometry.
4. The apparatus of claim 1 , wherein determining comprises determining electrical admittance spectra.
5. The apparatus of claim 4 , the one or more properties of the fluid comprising fluid density,
wherein fluid density (rho) is determined at least in part based on the equation
rho
=
α
1
(
DR
-
DPHBW
)
+
α
2
(
DI
2
-
DPHBW
)
+
α
3
DM
2
where DR denotes a peak shift in a real part of complex admittance between air and fluid, DPHBW denotes change in bandwidth between air and fluid, DI2 denotes the valley shift in the imaginary part of admittance between air and fluid, DM2 denotes the valley shift in admittance magnitude between air and fluid, and α1, α2, α3 denote regression coefficients.
6. The apparatus of claim 5 , wherein the one or more properties of the fluid further comprise fluid sound speed.
7. The apparatus of claim 6 ,
wherein fluid sound speed (SS) is determined at least in part based on the equation
ss
=
α
1
DPH
+
α
2
(
DR
-
DPHBW
)
+
α
3
DI
2
-
DPHBW
where DPH denotes a difference in phase peak of admittance between air and fluid, DR denotes a peak shift in the real part of admittance between air and fluid, DPHBW denotes change in bandwidth between air and fluid, DI2 denotes the valley shift in the imaginary part of admittance between air and fluid, and α1, α2, α3 denote regression coefficients.
8. The apparatus of claim 1 , wherein the leaf cell sensor comprises eight piezoelectric radial components.
9. The apparatus of claim 1 , wherein the leaf cell sensor comprises lead zirconate titanate.
10. The apparatus of claim 1 , wherein the circumferential component has an outer diameter of between 8 mm and 12 mm.
11. The apparatus of claim 1 , wherein the apparatus is integrated into a production logging tool or a logging while drilling tool, wherein the fluid comprises a multiphase wellbore fluid.
12. A method for measuring one or more properties of a fluid, the method comprising:
immersing the apparatus of claim 1 into a volume of the fluid;
applying electrical energy at multiple frequencies concurrently across the first electrode and the second electrode to induce strain in the piezoelectric radial component;
measuring, in response to inducing the strain, a current flowing between the first electrode and the second electrode; and
determining, from the current, the one or more properties of the fluid.
13. The method of claim 12 , wherein the electrical energy has a band-limited spectral power density with energy content concentrated at a particular range of frequencies.
14. The method of claim 12 , wherein determining comprises determining electrical admittance spectra.
15. The method of claim 12 , the one or more properties of the fluid comprising fluid density and fluid sound speed,
wherein the fluid density (rho) is determined at least in part based on the equation
rho
=
α
1
(
DR
-
DPHBW
)
+
α
2
(
DI
2
-
DPHBW
)
+
α
3
DM
2
where DR denotes a peak shift in a real part of complex admittance between air and fluid, DPHBW denotes change in bandwidth between air and fluid, DI2 denotes the valley shift in the imaginary part of admittance between air and fluid, DM2 denotes the valley shift in admittance magnitude between air and fluid, and α1, α2, α3 denote regression coefficients, and
wherein fluid sound speed (SS) is determined at least in part based on the equation
ss
=
α
1
DPH
+
α
2
(
DR
-
DPHBW
)
+
α
3
DI
2
-
DPHBW
where DPH denotes a difference in phase peak of admittance between air and fluid, DR denotes a peak shift in the real part of admittance between air and fluid, DPHBW denotes change in bandwidth between air and fluid, DI2 denotes the valley shift in the imaginary part of admittance between air and fluid, and α1, α2, α3 denote regression coefficients.
16. An apparatus for fluid measurement, the apparatus comprising:
a leaf cell sensor having one or more piezoelectric radial components connected to a circumferential component, the one or more radial components and the circumferential component having a distal face and a proximal face;
a first electrode positioned on the distal face of at least one radial component;
a second electrode positioned on the proximal face of the at least one radial component;
a voltage source having a negative terminal and a positive terminal, the negative terminal being connected to the first electrode and the positive terminal being connected to the second electrode;
an electric current measurement device connected to the first and second electrode to measure current flowing between the first and second electrode; and
a processor of a computing device and a non-transitory computer readable medium storing instructions thereon, wherein the instructions, when executed, cause the processor to determine, from the measured current, one or more properties of the fluid,
wherein the voltage source couples electrical energy into the one or more piezoelectric radial components at multiple frequencies concurrently, and
wherein the voltage source comprises a square wave pulse train.
17. A method for measuring one or more properties of a fluid, the method comprising:
immersing the apparatus of claim 16 into a volume of the fluid;
applying electrical energy at multiple frequencies concurrently across the first electrode and the second electrode to induce strain in the piezoelectric radial component;
measuring, in response to inducing the strain, a current flowing between the first electrode and the second electrode; and
determining, from the current, the one or more properties of the fluid.